Bonus: Fastest legal pick

A race with rules

Put the red ball in the cup as fast as you can. The catch: no command may ever ask a joint to exceed arm.vmax or arm.amax. Everything is unlocked (move_joints, move_to, arm.ik, arm.stream and your own profiles), and the limits are checked on every command of the run, whichever helper sent it.

The starter is the Pick & Place solution. It gets the ball in, but its transit to the cup swings the base at twice its speed limit.

Where the time goes

• move_joints and move_to use min-jerk timing over a duration you choose. With move_joints every joint follows the min-jerk curve, which peaks at $1.875\,|\Delta|/T$ in speed and $5.77\,|\Delta|/T^2$ in acceleration. move_to runs it along the Cartesian line instead, so its joint speeds depend on the path. Make $T$ too short and you break a limit; too long and you waste time.
• Your synchronised trapezoid from Step 4 is the fastest joint-space straight line there is, so reuse it.
• A straight Cartesian descent is the safe way onto a ball. Over a few centimetres, though, a joint-space move is almost straight too.
• The servos lag behind the commands. move_joints and move_to wait for them to catch up (for up to 0.6 s) before they return, and that wait costs time too. arm.stream and set_joint_targets don't wait, so after a fast streamed move give the servos a moment before you close the gripper, or the fingers will close next to the ball.
• gripper.close() and gripper.open() each wait for the fingers to move.

Your task

Grasp the red ball and release it over the cup, as early as you can. The ball must end up in the cup, and every command must respect the limits: speed within 2% and acceleration within 5%.

Bonus: open the gripper over the cup less than 5.2 s after the start.